Related papers: Diffusion on $\kappa$-Minkowski space
It is by now well established that the momentum space dual to the non-commutative $\kappa$-Minkowski space is a submanifold of de Sitter space. It has been noticed recently that field theories built on such momentum space suffer from a…
In this paper we introduce the systematic study of invariant functions and equivariant mappings defined on Minkowski space under the action of the Lorentz group. We adapt some known results from the orthogonal group acting on the Euclidean…
We give a quantum deformation of the chiral super Minkowski space in four dimensions as the big cell inside a quantum super Grassmannian. The quantization is performed in such way that the actions of the Poincar\'e and conformal quantum…
A useful concept in the development of physical models on the $\kappa$-Minkowski noncommutative spacetime is that of a curved momentum space. This structure is not unique: several inequivalent momentum space geometries have been identified.…
Starting from a classical-mechanics stochastic model encoded in a Langevin equation, we derive the natural diffusion equation associated with three classes of multiscale spacetimes (with weighted, ordinary, and "q-Poincar\'e" symmetries).…
This work provides an extension of parts of the classical finite dimensional sub-elliptic theory in the context of infinite dimensional compact connected metrizable groups. Given a well understood and well behaved bi-invariant Laplacian,…
Using the twist deformation of $U(igl(4,R))$, the linear part of the diffeomorphism, we define a scalar function and construct a free scalar field theory in four-dimensional $\kappa$-Minkowski spacetime. The action in momentum space turns…
We present explicit formulae for q-exponentials on quantum spaces which could be of particular importance in physics, i.e. the q-deformed Minkowski-space and the q-deformed Euclidean space with two, three or four dimensions. Furthermore,…
A regular spectral triple is proposed for a two-dimensional $\kappa$-deformation. It is based on the naturally associated affine group $G$, a smooth subalgebra of $C^*(G)$, and an operator $\caD$ defined by two derivations on this…
We determine the extent to which certain classes of fractionally `smooth' continuous mappings between metric spaces distort various dimensions, including the Hausdorff, upper Minkowski (box-counting), and upper intermediate dimensions. Our…
We prove a refined contraction inequality for diffusion semigroups with respect to the Wasserstein distance on a compact Riemannian manifold taking account of the dimension. The result generalizes in a Riemannian context, the dimensional…
When considering Navier-Stokes equations on Riemannian manifolds one frequently encounters situations where the manifold is embedded in the ambient Euclidean space. In this context it is interesting to investigate what is the precise…
It is shown that application of dynamic flows concept in 4-dimensional Euclidean space makes possible to form Minkowski space and to formulate the generalized variational problem of electrodynamics and gravi- dynamics. It is shown that…
We give a quantum deformation of the chiral Minkowski superspace in 4 dimensions embedded as the big cell into the chiral conformal superspace. Both deformations are realized as quantum homogeneous superspaces: we deform the ring of regular…
The formulation of combinatorial differential forms, proposed by Forman for analysis of topological properties of discrete complexes, is extended by defining the operators required for analysis of physical processes dependent on scalar…
The bicovariant differential calculus on the four-dimensional kappa-Poincare group and the corresponding Lie-algebra like structure are described. The deifferential calculus on the n-dimensional kappa-Minkowski space covariant under the…
In this paper, we consider a Lewy-Stampacchia-type inequality for the fractional Laplacian on a bounded domain in Euclidean space. Using this inequality, we can show the well-posedness of fractional-type anomalous unidirectional diffusion…
We investigate a Lie algebra-type $ \kappa$-deformed Minkowski space-time with undeformed Lorentz algebra and mutually commutative vector-like Dirac derivatives. There are infinitely many realizations of $ \kappa$-Minkowski space. The…
In this article we present explicit formulae for q-differentiation on quantum spaces which could be of particular importance in physics, i.e., q-deformed Minkowski space and q-deformed Euclidean space in three or four dimensions. The…
We present Manifold Diffusion Fields (MDF), an approach that unlocks learning of diffusion models of data in general non-Euclidean geometries. Leveraging insights from spectral geometry analysis, we define an intrinsic coordinate system on…